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Abstract and Applied Analysis
Volume 2012, Article ID 303706, 12 pages
http://dx.doi.org/10.1155/2012/303706
Research Article

The Lie Brackets on Time Scales

Department of Mathematics, Faculty of Sciences, Ege University, 35100 Izmir, Turkey

Received 7 May 2012; Accepted 26 June 2012

Academic Editor: Natig Atakishiyev

Copyright © 2012 H. Kusak and A. Caliskan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Lie derivative, which has a wide range of application in physics and geometry, is trying to be examined on time scales. Firstly, nabla Lie bracket is defined on two-dimensional time scales. Secondly, the nabla Lie multiplication and some properties are given on the time scales. Lastly, for analyzing the differences between the real Lie multiplication and the nabla Lie multiplication, a numerical example is given.